400-600 yards isn't so far that it takes even a .223/5.56 out of the running for prairie dogs. I shoot quite a bit in windy conditions over prairie dog fields and have used both 5.56 and 22-250 to good effect at those distances and beyond. While the .223/5.56 works just fine, the 22-250 is easier to shoot in the wind. A scope reticle with wind holds or, at a minimum, mil/moa hash marks and matching turrets is very useful for spotting and adjusting for misses.
I would be looking at a factory rifle of your choice in .223/5.56, 22-250, or .243, shooting Hornady Superformance Varmint as my first choice of ammo. This will buy you 53 VMAX @ 3465 in .223, 50 VMAX @ 4000 in 22-250, and 58 VMAX @ 3925 or 75 VMAX @ 3580 in .243 Win. If the chosen rifle doesn't like Superformance, the standard Varmint Express typically does very well.
The .204 Ruger may also deserve consideration, but I don't have any personal experience with it.